cannot export .glb with material setting like specular
glTF 2.0's core material system uses the metallic + roughness PBR system.  You are correct that the specular channel is not currently included.  This may change in a future version of Blender, as there is a newer glTF extension proposal for including it inside of the metal/rough workflow.  But it could be some time before that appears in Blender's importer/exporter for glTF.
In the meantime, for this model you may be able to work around this by setting Roughness to 1.0.  That should make the material diffuse enough to not show any specular reflection.